The headteacher of a boy who died with his father while hiking in the Alps has paid tribute to the 12-year-old as "a talented and very motivated boy who made a huge impact on the lives of everyone who knew him".

Charlie Saunders and his father Peter, 48, died on Saturday afternoon while exploring a trail in the Couloir des Bossons on the Mont Blanc range above the Chamonix valley. The popular route is perilously slippery and often impossible to follow when covered in snow and ice in winter.

The two bodies were discovered together by a rescue team early on Sunday morning. The father apparently fell to his death while trying to save his child.

David Hudson, headteacher at Charlie's school, the Royal Latin in Buckingham, said: "He was a popular boy and threw himself into school life with 100% effort. Charlie loved a wide range of sports and especially the great outdoors. He will be hugely missed and we send our thoughts and prayers to his family, especially his mother and sister, at this tragic time."

The rest of the family were not on the weekend break but are expected to travel to the area soon.

The rescue centre at Annecy received a brief call from the father at around 3pm on Saturday, saying that his son had fallen and disappeared.

"He said he could no longer see him and couldn't get to him," said Captain Patrice Ribes, the deputy commander of the mountain rescue gendarmerie at Chamonix. "We think the father tried to find his son after he called us and asked for rescue. We believe he fell as he tried to find his son."

The gendarmerie said the father told them he was near Les Houches, a village next to Chamonix. The gendarme who took the call tried to ask the man some questions to find out his exact location but "he was very, very panicked and then the line was cut". The gendarmerie tried to call back, but were immediately diverted to voicemail.

"The conversation was very brief. We believe the father died very quickly after his son, possibly trying to rescue him," a gendarmerie spokesman said.

A rescue mission was launched, but gendarmes said the search area was immense and that they were initially unsure whether the pair were skiing, walking with snowshoes, or on foot.

Mobile telephone operators were asked to check their records to help establish the father's location and identity.

British police were contacted through Interpol to help confirm identities and to inform family members, who gave details of where the pair planned to walk. The search was called off at nightfall, but work on narrowing down the location of the accident continued through the night.

"Thanks to a photograph the father sent on Saturday we were able to identify the place where we should be searching around 2am on Sunday," said Ribes.

The search resumed at first light, and the bodies were discovered 40 minutes later at 7.40am in a corridor around Bossons. The boy had fallen about 300 metres into the corridor while his father had fallen 200 metres.

The pair had flown to Geneva on Saturday to spend the weekend in Chamonix. According to locals the walking route they chose is popular in summer, but not in winter, when it needs to be traversed with special equipment.

"They could have got lost, because in winter you can't see the path because it disappears under the snow as it crosses the corridors and one can very easily fall," said Ribes. "It's a slide of snow and ice, with rocky ledges at regular intervals and if you don't have crampons or icepicks, it's impossible to stop."

He said the pair had been equipped for a day walk, with "trekking-type shoes with tread soles that are not suitable for a snow- and ice-covered winter mountain".

But the policeman stressed it was too early to say what had happened. "An inquiry will establish the circumstances of the accident, as well as the level of preparation and experience of the walkers," he said. "Every death on the mountain is different."

Richard Mansfield, a mountain guide who has worked in the area for 20 years and lives less than a mile (1km) from the Bossons glacier, said: "I don't know exactly where the accident happened but all the trails on the north side of the valley are covered in snow at the moment.

"The footpaths usually don't get that many people out at this time of year because they are much more difficult to navigate, although yesterday was a beautiful sunny day."

The valley, which boasts five ski resorts, receives a lot of British tourists throughout the year, with many owning holiday homes in the area.